Refractive index interactions

The Hamaker constant can be evaluated accurately using tire continuum tlieory, developed by Lifshitz and coworkers [40]. A key property in tliis tlieory is tire frequency dependence of tire dielectric pennittivity, (cij). If tills spectmm were tlie same for particles and solvent, then A = 0. Since tlie refractive index n is also related to f (to), tlie van der Waals forces tend to be very weak when tlie particles and solvent have similar refractive indices. A few examples of values for A for interactions across vacuum and across water, obtained using tlie continuum tlieory, are given in table C2.6.3. 

Solvents exert their influence on organic reactions through a complicated mixture of all possible types of noncovalent interactions. Chemists have tried to unravel this entanglement and, ideally, want to assess the relative importance of all interactions separately. In a typical approach, a property of a reaction (e.g. its rate or selectivity) is measured in a laige number of different solvents. All these solvents have unique characteristics, quantified by their physical properties (i.e. refractive index, dielectric constant) or empirical parameters (e.g. ET(30)-value, AN). Linear correlations between a reaction property and one or more of these solvent properties (Linear Free Energy Relationships - LFER) reveal which noncovalent interactions are of major importance. The major drawback of this approach lies in the fact that the solvent parameters are often not independent. Alternatively, theoretical models and computer simulations can provide valuable information. Both methods have been applied successfully in studies of the solvent effects on Diels-Alder reactions. 

Fundamental Limitations to Beers Law Beer s law is a limiting law that is valid only for low concentrations of analyte. There are two contributions to this fundamental limitation to Beer s law. At higher concentrations the individual particles of analyte no longer behave independently of one another. The resulting interaction between particles of analyte may change the value of 8. A second contribution is that the absorptivity, a, and molar absorptivity, 8, depend on the sample s refractive index. Since the refractive index varies with the analyte s concentration, the values of a and 8 will change. For sufficiently low concentrations of analyte, the refractive index remains essentially constant, and the calibration curve is linear. 

Equations (10.17) and (10.18) show that both the relative dielectric constant and the refractive index of a substance are measurable properties of matter that quantify the interaction between matter and electric fields of whatever origin. The polarizability is the molecular parameter which is pertinent to this interaction. We shall see in the next section that a also plays an important role in the theory of light scattering. The following example illustrates the use of Eq. (10.17) to evaluate a and considers one aspect of the applicability of this quantity to light scattering. 

Many of the unusual properties of the perfluorinated inert fluids are the result of the extremely low intermolecular interactions. This is manifested in, for example, the very low surface tensions of the perfluorinated materials (on the order of 9-19 mN jm. = dyn/cm) at 25°C which enables these Hquids to wet any surface including polytetrafluoroethene. Their refractive indexes are lower than those of any other organic Hquids, as are theh acoustic velocities. They have isothermal compressibilities almost twice as high as water. Densities range from 1.7 to 1.9 g/cm (l )-... 

Polarizability Attraction. AU. matter is composed of electrical charges which move in response to (become electrically polarized in) an external field. This field can be created by the distribution and motion of charges in nearby matter. The Hamaket constant for interaction energy, A, is a measure of this polarizability. As a first approximation it may be computed from the dielectric permittivity, S, and the refractive index, n, of the material (15), where is the frequency of the principal electronic absorption... 

Suspended particles are the most important factor in visibility reduction. In most instances, the visual quality of air is controlled by partide scattering and is characterized by the extinction coeffident The size of particles plays a crucial role in their interaction with light. Other factors are the refractive index and shape of the particles, although their effect is harder to measure and is less well understood. If we could establish these properties, we could calculate the amount of light scattering and absorption. Alternatively, the extinction coeffident associated with an aerosol can be measured directly. 

The real component of the neutron refractive index 8 is related to the wavelength X of the incident neutrons, the neutron scatterir length (a measme of the extent to which neutrons interact with different nuclei), the mass density and the atomic... 

The refractive index of a medium is the ratio of the speed of light in a vacuum to its speed in the medium, and is the square root of the relative permittivity of the medium at that frequency. When measured with visible light, the refractive index is related to the electronic polarizability of the medium. Solvents with high refractive indexes, such as aromatic solvents, should be capable of strong dispersion interactions. Unlike the other measures described here, the refractive index is a property of the pure liquid without the perturbation generated by the addition of a probe species. 

The theory of counterion condensation is implicit in Oosawa (1957) but the term was coined later (Imai, 1961). The phenomenon was demonstrated by Ikegami (1964), using refractive index measurements of the interaction between sodium and polyacrylate ions. It has since been confirmed for many mono-, di- and trivalent counterions and polyionic species (Manning, 1979). 

In this Section we want to present one of the fingerprints of noble-metal cluster formation, that is the development of a well-defined absorption band in the visible or near UV spectrum which is called the surface plasma resonance (SPR) absorption. SPR is typical of s-type metals like noble and alkali metals and it is due to a collective excitation of the delocalized conduction electrons confined within the cluster volume [15]. The theory developed by G. Mie in 1908 [22], for spherical non-interacting nanoparticles of radius R embedded in a non-absorbing medium with dielectric constant s i (i.e. with a refractive index n = Sm ) gives the extinction cross-section a(o),R) in the dipolar approximation as ... 

Figure 6. Absorption spectra of spherical non-interacting nanoclusters embedded in no absorbing matrices (a) effect of the size for Ag nanoclusters in silica (b) effect of the matrix for R = 2.5 nm Au clusters (the refractive index n = and the position of the plasma resonance are reported for each considered matrix) (c) effect of the cluster composition for i = 5 nm noble-metal clusters (Ag, Au, Cu) in silica. (Reprinted from Ref [1], 2005, with permission from Italian Physical Society.)...

The dielectric constant and refractive index parameters and different functions of them that describe the reactive field of solvent [45] are insufficient to characterize the solute-solvent interactions. For this reason, some empirical scales of solvent polarity based on either kinetic or spectroscopic measurements have been introduced [46,47]. The solvatochromic classification of solvents is based on spectroscopic measurements. The solvatochromic parameters refer to the properties of a molecule when its nearest neighbors are identical with itself, and they are average values for a number of select solutes and somewhat independent of solute identity. 

It is important to know the influence of the physicochemical parameters of the mobile phase (dipole moment, dielectric constant, and refractive index) on solvent strength and selectivity. The main interactions in planar chromatography between the molecules of the mobile phases and those of solutes are caused by dispersion forces related to the refractive index, dipole-dipole forces related to the dipole moment, induction forces related to a permanent dipole and an induced one, hydrogen bonding, and dielectric interactions related to the dielectric constant. Solvent strength depends mainly on the dipole moment of the mobile phase, whereas the solvent selectivity depends on the dielectric constant of the mobile phase. 

---